In this study, we investigate the influence of fine-scale changes in the elevation of urban terrains on the dynamics and final distribution of flood inundation generated by intense rainfall. Numerical experiments have been performed combining two-dimensional shallow water model with extremely fine-resolution (10 cm) terrain data. Our results reveal that localised, decimetric-scale alterations in the elevation of streets can lead to remarkable differences in the flood inundation. These results confirm the important role played by finely resolved and accurate terrain data in capturing flow patterns that have a central impact on model predictions of flood inundation. Also, we argue that the observed sensitivity of flood inundation to small-scale topographical features paves the way to new opportunities for flood risk management measures. In particular, engineering flood resilient urban surfaces using fine-resolution models has a potential to considerably reduce flood impacts at a relatively low cost.